Their personal skills Fire Blessing are almost the same, differing only in casting time and action time. All skills are at Lv.10, except for the first skill (i.e. Lv.8 Flame Dance and Quick Boom).

The two stances have 3 similar skills, so I will compare them with each other: Flame Dance vs. Quick Boom, Flame Hammer vs. Flame Mallet, and Magma Storm vs. Meteor Shower. The 2 strongest skills will match each other - Breath of Flame vs. Flame Rampage and Fire Vrille vs. Summon Sekhmet.

Infernal Burn skills deal more damage than Efreet skills, except for Meteor Shower vs. Magma Storm. Although Meteor Shower has no casting time, Magma Storm has only 1s casting time, so the difference might not be significant.

Another issue for Efreet is that Fire Vrille is a line effect, which isn't always easy to hit the targets. On the other hand, Summon Sekhmet is an circle effect auto-centered on the caster.

In addition to doing more damage, Flame Rampage (12s) has a much shorter cooldown than Breath of Flame (90s), making the former more spammable. Flame Rampage is a single target skill, similar to Ion's Frost Dust, while Breath of Flame affects a fan-shaped area.

CONCLUSIONS

Blue Flame Ludin is stronger than Ludin in both normal attacks and most skills (except for Meteor Shower).